\[{\overline{C}\ }_{8}^{3} = \frac{(3 + 8 - 1)!}{3!(8 - 1)!} = \frac{10!}{3! \bullet 7!} =\]
\[= \frac{10 \bullet 9 \bullet 8 \bullet 7!}{3 \bullet 2 \bullet 7!} = 5 \bullet 3 \bullet 8 =\]
\[= 120\ параллелепипедов.\]
\[Ответ:\ \ 120.\]